ZETA-FUNCTIONS AND TRANSFER OPERATORS FOR PIECEWISE MONOTONE TRANSFORMATIONS

Given a piecewise monotone transformation T of the interval and a piecewise continuous complex weight function g of bounded variation, we prove that the Ruelle zeta function ζ(z) of (T, g) extends meromorphically to {{divides}z{divides}<θ-1} (where θ=lim ∥g°Tn-1...g°Tg∥∞1/n) and that z is a pole of ζ if and only if z-1 is an eigenvalue of the corresponding transfer operator L. We do not assume that L leaves a reference measure invariant. © 1990 Springer-Verlag.